Ask question

Ask question

All categories

SCORPION-xisa [38]

3 years ago

8

Hello I need help with this, Don Manuel has 600m of fence to build a rectangular-shaped corral. You will take advantage of a ver

y long wall as one of the sides of the pen, that is, on the side of the wall you will not use fence. What should be the dimensions of the pen with maximum area among all those that use 600m of fence?

1 answer:

Anton [14]3 years ago

5 0

Answer: If the wall is 300 meters long, the dimensions of the fence with the maximum area will be 300 × 150 = 45000 m²

Step-by-step explanation:

try combinations in a chart

190 × (600-190)/2 = 38950 = 190 × 205 increasing area

200 × (600-200)/2 = 40000 = 200 × 200

220 × (600-220)/2 = 41800 == 220 × 190

240 × (600-240)/2 = 43200 == 240 × 180

260 × (600-260)/2 = 44200 == 260 × 170

280 × (600-280)/2 = 44800 . == 280 × 160

<u>300 × (600-300)/2 = 45000 == 300 × 150</u> Maximum Area

310 × (600-310)/2 = 44950 . == 310 × 145 decreasing area

320 × (600-320)/2 = 44800 . == 320 × 140

You might be interested in

Is 1,384 a rational number

ycow [4]

Answer: Should be rational

hope this helps.

3 0

3 years ago

Read 2 more answers

Two-fifths of the students in 6th grade are in the band, Of these, one-

Gelneren [198K]

Answer:

1/10 or 10%

Step-by-step explanation:

1/4 x 2/5 = 1/10 (10%)

3 0

3 years ago

Find the value of x and the length of both chords if BW=2x+10, WD=4, CW=7x+5, and WE=2.

daser333 [38]

Answer:

The value of x is 5

The lengths of the chords are 24 units and 42 units

Step-by-step explanation:

In a circle if two chords intersected at a point inside it there are four segments created, two in each cord, the products of the lengths of the line segments on each chord are equal

∵ BD and CE are two chords in a circle intersected at W

∴ The two segments of chord BD are BW and WD

∴ The two segments of chord CE are CW and WE

- By using the rule above

∴ BW × WD = CW × WE

∵ BW = 2x + 10 and WD = 4

∵ CW = 7x + 5 and WE = 2

- Substitute them in the rule above

∴ (2x + 10) × 4 = (7x + 5) × 2

∴ 4(2x) + 4(10) = 2(7x) + 2(5)

∴ 8x + 40 = 14x + 10

- Subtract 14x from both sides

∴ - 6x + 40 = 10

- Subtract 40 from both sides

∴ - 6x = - 30

- Divide both sides by - 6

∴ x = 5

∵ Chord BD = 2x + 10 + 4

∴ Chord BD = 2x + 14

- Substitute the value of x to find its length

∴ Chord BD = 2(5) + 14 = 10 + 14

∴ Chord BD = 24 units

∵ Chord CE = 7x + 5 + 2

∴ Chord CE = 7x + 7

- Substitute the value of x to find its length

∴ Chord CE = 7(5) + 7 = 35 + 7

∴ Chord CE = 42 units

5 0

3 years ago

A foreign student club lists as its members 2 Canadians, 3 Japanese, 5 Italians, and 2 Germans. If a committee of 4 is selected

Fittoniya [83]

Answer:

(a) The probability that the members of the committee are chosen from all nationalities $=\frac{4}{33}$ =0.1212.

(b)The probability that all nationalities except Italian are represent is 0.04848.

Step-by-step explanation:

Hypergeometric Distribution:

Let $x_1$ , $x_2$ , $x_3$ and $x_4$ be four given positive integers and let $x_1+x_2+x_3+x_4= N$ .

A random variable X is said to have hypergeometric distribution with parameter $x_1$ , $x_2$ , $x_3$ , $x_4$ and n.

The probability mass function

$f(x_1,x_2.x_3,x_4;a_1,a_2,a_3,a_4;N,n)=\frac{\left(\begin{array}{c}x_1\\a_1\end{array}\right)\left(\begin{array}{c}x_2\\a_2\end{array}\right) \left(\begin{array}{c}x_3\\a_3\end{array}\right) \left(\begin{array}{c}x_4\\a_4\end{array}\right) }{\left(\begin{array}{c}N\\n\end{array}\right) }$

Here $a_1+a_2+a_3+a_4=n$

${\left(\begin{array}{c}x_1\\a_1\end{array}\right)=^{x_1}C_{a_1}= \frac{x_1!}{a_1!(x_1-a_1)!}$

Given that, a foreign club is made of 2 Canadian members, 3 Japanese members, 5 Italian members and 2 Germans members.

$x_1$ =2, $x_2$ =3, $x_3$ =5 and $x_4$ =2.

A committee is made of 4 member.

N=4

(a)

We need to find out the probability that the members of the committee are chosen from all nationalities.

$a_1$ =1, $a_2$ =1, $a_3$ =1 , $a_4$ =1, n=4

The required probability is

$=\frac{\left(\begin{array}{c}2\\1\end{array}\right)\left(\begin{array}{c}3\\1\end{array}\right) \left(\begin{array}{c}5\\1\end{array}\right) \left(\begin{array}{c}2\\1\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }$

$=\frac{2\times 3\times 5\times 2}{495}$

$=\frac{4}{33}$

=0.1212

(b)

Now we find out the probability that all nationalities except Italian.

So, we need to find out,

$P(a_1=2,a_2=1,a_3=0,a_4=1)+P(a_1=1,a_2=2,a_3=0,a_4=1)+P(a_1=1,a_2=1,a_3=0,a_4=2)$

$=\frac{\left(\begin{array}{c}2\\2\end{array}\right)\left(\begin{array}{c}3\\1\end{array}\right) \left(\begin{array}{c}5\\0\end{array}\right) \left(\begin{array}{c}2\\1\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }+\frac{\left(\begin{array}{c}2\\1\end{array}\right)\left(\begin{array}{c}3\\2\end{array}\right) \left(\begin{array}{c}5\\0\end{array}\right) \left(\begin{array}{c}2\\1\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }$ $+\frac{\left(\begin{array}{c}2\\1\end{array}\right)\left(\begin{array}{c}3\\1\end{array}\right) \left(\begin{array}{c}5\\0\end{array}\right) \left(\begin{array}{c}2\\2\end{array}\right) }{\left(\begin{array}{c}12\\4\end{array}\right) }$

$=\frac{1\times 3\times 1\times 2}{495}+\frac{2\times 3\times 1\times 2}{495}+\frac{2\times 3\times 1\times 1}{495}$

$=\frac{6+12+6}{495}$

$=\frac{8}{165}$

=0.04848

The probability that all nationalities except Italian are represent is 0.04848.

6 0

3 years ago

There are three different cubes such that the first cube is 64 times the volume of the second, and the volume of the second cube

tankabanditka [31]

Answer:

4/3

Step-by-step explanation:

If the ratio between the volumes of the first and the second cube is 64, the ratio between the sides is the cubic root of the ratio between the volumes, so:

$V1 / V2 = 64$

$s1 / s2 = \sqrt[3]{64} = 4$

Doing the same for the second and third cubes, we have:

$V2 / V3 = 1/27$

$s2/ s3 = \sqrt[3]{1/27} = 1/3$

So the ratio of the first cube side and the third cube side is:

$s1 / s3 = (s1/s2) * (s2/s3) = 4 * (1/3) = 4/3$

5 0

3 years ago